Computing Green currents via the heat kernel (Q2754270)

Let \(X\) be a compact Kähler manifold. We show that there exists a unique Green current \(g_Y\) for any cycle \(Y\) in \(X\). We show that the current \(g_Y\) is a form with \(L^1\)-coefficients. The heat kernel applied to the Dirac distribution associated with \(Y\) plays a central role in this construction. Furthermore, we show how these Green currents fit into intersection theory. Finally, we compute this canonical current for some examples.